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Minimal Nonsquare J-Spectral Factorization, Generalized Bezoutians and Common Zeros for Rational Matrix Functions

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Abstract.

The problem that we solve in this paper is to find (square or nonsquare) minimal J-spectral factors of a rational matrix function with constant signature. Explicit formulas for these J-spectral factors are given in terms of a solution of a particular algebraic Riccati equation. Also, we discuss the common zero structure of rational matrix functions that arise from the analysis of nonsquare J-spectral factors. This zero structure is obtained in terms of the kernel of a generalized Bezoutian.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Potchefstroom University for CHE, X 6001, Potchefstroom, South Africa

    Mark A. Petersen

  2. Divisie Wiskunde en Informatica, Faculteit Wiskunde en Informatica, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081, HV Amsterdam, The Netherlands

    André C.M. Ran

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  1. Mark A. Petersen
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  2. André C.M. Ran
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Correspondence to Mark A. Petersen.

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Petersen, M.A., Ran, A.C. Minimal Nonsquare J-Spectral Factorization, Generalized Bezoutians and Common Zeros for Rational Matrix Functions. Integr. equ. oper. theory 47, 197–216 (2003). https://doi.org/10.1007/s00020-002-1159-y

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  • DOI: https://doi.org/10.1007/s00020-002-1159-y

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